This invention generally relates to interferometry and more particularly to apparatus and methods for interferometrically measuring with high accuracy the position and angular orientation of a body as it travels along a nominally straight line in, for example, a process for determining the shape of optical surfaces such as aspherical surfaces and wavefronts.
Aspherical surfaces have become more and more important in modern optical systems because they offer a higher number of parameters for simplifying systems while optimizing their performance. This can lead to systems with less surfaces, less weight, smaller dimensions and higher states of correction, to mention only a few advantages. This is especially true in fields where a high number of optical surfaces are not practical, like in astronomical telescopes or normal incidence reflecting surfaces for the EUV wavelength of 13.6 nm used for lithography tools, where it is mandatory to keep the number of surfaces as low as possible. In such cases, there is no choice but to use aspherical surfaces. With demands for high quality performance for complete systems operating in the EUV-regime, the surface errors of reflecting surfaces within such a system must be kept below 0.1 nm rms, and the measuring accuracy and precision for such errors must be even higher to be able to produce the surfaces in a deterministic manner. In addition, lens surfaces in multi-element lithography lenses operating at wavelengths of 193 nm and 157 nm are made aspherical to lower the number of elements made, which are of rare and expensive materials. In these cases, the departures from a best fitting sphere can be as large as 1000 μm or more, and the dimensions of such lens surfaces have increased to nearly 500 mm.
In an optical system, the function of any its lens elements is to modify the wavefront transmitted by the individual lens elements according to the optical design of the whole system. If a spherical wave or a plane wave enter such a lens, an aspherical wavefront with a very high departure from the best fitting sphere is produced, depending on the conjugates used in the particular test-configuration. So even the fundamental single lens element with either spherical or aspherical surfaces can only be tested properly if one is able to deal with aspherical wavefronts in a test set-up. Moreover, this ability is very important for testing wavefronts transmitted through lens elements because inhomogeneity of the lens material itself can deteriorate the wavefront, even when the surfaces are otherwise free of error.
The measurement of aspherical surfaces and wavefronts has been very difficult because of the large departure from the best fitting sphere. With interferometric measurements, high precision is achieved by making the dynamic range of the measurement very small, and for this purpose, the wavefront of the reference wavefront, against which the aspherical wavefront is compared, has to be made aspherically as well to ideally fit the wavefront to be measured completely.
Recently, interferometric scanning method(s) and apparatus have been developed for measuring rotationally and non-rotationally symmetric test optics either having aspherical surfaces or that produce aspherical wavefronts. In such scanning method(s) and apparatus, a spherical or partial spherical wavefront is generated from a known origin along an optical or scan axis. The test optic is aligned with respect the scanning axis and selectively moved along it along a nominally straight line relative to the known origin so that the spherical wavefront intersects the test optic at the apex of the aspherical surface and at radial positions where the spherical wavefront and the aspheric surface intersect at points of common tangency. An axial distance, ν, and optical path length, p, are interferometrically measured as the test optic is axially scanned by the spherical wavefront where ν is the distance by which the test optic is moved with respect to the origin and p is the optical path length difference between the apex of an aspherical surface associated with the test optic and the apex of the circles of curvature that intersect the aspherical surface at the common points of tangency. Coordinates of the aspherical surface are calculated wherever the circles of curvature have intersected the aspherical surface and in correspondence with the interferometrically measured distances, ν and p. Afterwards, the shape of the aspheric surface is calculated. Where the test optic comprises a refracting optic a known spherical reflecting surface is provided upstream of the refracting optic for movement along the optical axis and a known wavefront is made to transit the refracting optic, reflects from the known spherical surface, again transits the refracting optic traveling towards the known origin after which the interferogram is formed (See, e.g., U.S. Provisional Patent Application No. 60/303,856 filed on Jul. 9, 2001 in the name of Michael Küchel entitled “SCANNING INTERFEROMETER FOR ASPHERIC SURFACES AND WAVEFRONTS”, now U.S. patent application Ser. No. 10/180,285 filed on Jun. 26, 2002).
With such scanning methodologies, as well as for other distance and angle measuring applications, it is extremely important to be able to know to high accuracy what the relative position is between the test optic and the source of the scanning wavefront as the two are moved relative to one another. To determine the shape of optical surfaces to submicron accuracy, it is desirable to be able to measure the position of the various elements of such scanning applications with respect to the scan axis to subnanometer accuracy, and it is a primary object of the present invention to provide method(s) and apparatus by which this can be achieved.
It is another object of this invention to provide method(s) and apparatus for interferometrically measuring relative or absolute distances with high accuracy.
It is another object of the invention to provide method(s) and apparatus for interferometrically measuring slopes, curvatures, and shapes of optics with high accuracy.
It is still another object of the present invention to provide interferometric method(s) and apparatus for high accuracy measurement using redundant, self-checking metrology of the straightness of motion of a moving element along its travel.
Another object of this invention is to provide comparative, self-checking methods for calibrating the straightness of a scanning path in an interferometer.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the following description is read in connection with the drawings.